Question

A bond has a par value of $1,000, a time to maturity of 20 years, and a coupon rate of 7.10% with interest paid annually. If the current market price is $710, what will be the approximate capital gain of this bond over the next year if its yield to maturity remains unchanged? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Capital gain ___$

Answer 1

Step-1:Calculation of yield to maturity
	Yield to Maturity		=	Average income / Average Investment
			=	(Coupon+(Par Value-Current Price)/Life)/((Par Value + Current Price)/2)
			=	(71+(1000-710)/20)/((1000+710)/2)
			=	10.00%
	Working:
	Par Value					$    1,000
	Coupon		$    1,000	x 7.10%	=	$          71
Step-2:Calculation of Price after year 1
	Price of coupon is the present value of cash flow from bond.
	Present Value of annuity of 1			=	(1-(1+i)^-n)/i			Where,
				=	(1-(1+0.10)^-19)/0.10			i	10%
				=	8.3649			n	19
	Present Value of 1			=	(1+i)^-n
				=	(1+0.10)^-19
				=	0.1635
	Present Value of coupon			$             71	x	8.3649	=	593.91
	Present Value of Par Value			$       1,000	x	0.1635	=	163.51
	Price 1 year from now							757.42
Step-3:Calculation of Capital gain yield over the year
	Capital Gain yield		=	(Price after 1 - Current Price)/Current Price
			=	(757.42-710)/710
			=	6.68%
Thus,
Capital gain yield is 6.68%